Fig. 1 shows a smart meter display after a household has used electricity overnight. The display records energy in kilowatt-hours, not the number of applian...
Question 1 Report
Fig. 1 shows a smart meter display after a household has used electricity overnight. The display records energy in kilowatt-hours, not the number of appliances used. The home has an electric storage heater which is programmed to run when electricity is cheaper. The meter reading at 22:00 was 18 426.7 kWh. At 06:00 it was 18 438.9 kWh. The electricity company charges 24 p for each kilowatt-hour used.
(a) Calculate the energy transferred between 22:00 and 06:00. [2]
(b) Calculate the cost of this energy in pence. [2]
(c) What unit is used by the meter to measure electrical energy? [1]
A local library replaces old filament lamps with LED lamps. Fig. 1 compares two lamps that give similar light output. The librarian wants to lower the amount of electrical energy transferred each evening without making the reading area too dark. Both types of lamp are connected to the same 230 V supply, but their power ratings are different. The LEDs are used for six hours on each day that the library is open.
(a) Which lamp transfers electrical energy at the lower rate? [1]
(b) Calculate the energy used by one LED lamp in six hours. Give your answer in kWh. [2]
(c) Describe why fitting LEDs can reduce the library electricity bill. [2]
Answer Details
Smart meter
- (a) Energy transferred is the change in meter reading:
\[18438.9-18426.7=12.2\text{ kWh}\] [2] - (b) \[\text{cost}=12.2\text{ kWh}\times24\text{ p per kWh}=292.8\text{ p}\]
This may be given as \(293\text{ p}\) to the nearest penny. [2] - (c) The meter measures energy in kilowatt-hours, \(\text{kWh}\). [1]
Library lamps
- (a) The LED lamp transfers electrical energy at the lower rate because its power is 9 W, compared with 60 W. [1]
- (b) \(9\text{ W}=0.009\text{ kW}\).
\[E=Pt=0.009\times6=0.054\text{ kWh}\] [2] - (c) LEDs have lower power. Therefore, for the same operating time and similar light output, they transfer and use less electrical energy, reducing the electricity bill. [2]
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